Question

2. În tabelul următor am notat cu a, b, c, d, A, A şi lungimea bazei, lățimea bazei, înălțimea, diagonala, aria laterală, aria totală şi volumul unui paralelipiped dreptunghic. Completați tabelul, ştiind că dimensiunile sunt măsurate în centimetri.

Answer 1

$A_l=P_b\times h$

$A_t=2A_b+A_l$

$V=A_b\times h$

$d=\sqrt{l^2+L^2+h^2}$

a.

l=6

L=6√3

h=9

$d=\sqrt{36+108+81} =\sqrt{225}=15cm$

$P_b=2L+2l=12\sqrt{3} +12$

$A_l=9(12\sqrt{3} +12)\\\\A_t=9(12\sqrt{3} +12)+2\times 36\sqrt{3} =108+108\sqrt{3} +72\sqrt{3} =108+180\sqrt{3}$

$V=36\sqrt{3} \times 9=324\sqrt{3} cm^3$

b.

l=12

h=15

d=25

$625=225+144+L^2\\\\L^2=256\\L=16cm$

$A_b=16\times 12=192cm^2\\\\P_b=32+24=56cm\\A_l=56\times 15=840cm^2\\\\V=192\times 15=2880cm^3$

$A_t=840+384=1224cm^2$

c.

l=9

L=12

d=25

$625=81+144+h^2\\\\h=20cm$

$P_b=18+24=42cm\\\\A_b=108cm^2\\A_l=42\times 20=840cm^2\\\\V=108\times 20=3160cm^3\\A_t=216+840=1056cm^2$

d.

L=5

h=20

d=21

$441=25+400+l^2\\\\l=4cm$

$P_b=10+8=18cm\\A_b=20cm^2\\V=20\times 20=400cm^3\\A_l=18\times 20=360cm^2\\A_t=400+360=760cm^2$

e.

L=24

l=12

Al=792

$P_b=48+24=72cm\\\\h=792:72=11cm\\\\d=\sqrt{121+576+144} =29cm$

$A_b=288cm^2\\V=288\times 11=3168cm^3\\A_t=576+792=1368cm^2$

f.

l=12

L=24

V=6048

$A_b=288cm^2\\h=6048:288=21cm\\\\d=\sqrt{441+144+576} =\sqrt{1161} =3\sqrt{129}$

$P_b=72cm\\\\A_l=72\times 21=1512cm^2\\A_t=1512+576=2088cm^2$

g.

l=6

h=10

V=480

$A_b=480:10=48cm^2\\\\L=48:6=8cm\\\\P_b=16+12=28cm\\\\A_l=28\times 10=280cm^2\\A_t=280+96=376cm^2$

$d=\sqrt{36+64+100} =10\sqrt{2} cm$

h.

l=10

Al=264

At=504

Ab=(504-264):2=120cm²

L=120:10=12cm

Pb=44cm

$h=264:44=6cm$

V=120×6=720cm³

$d=\sqrt{100+144+36} =2\sqrt{70} cm$